In Green’s function diakoptics, wavefield interactions between disjoint domains in space are described in terms of interacting multi-port subsystems In addition to integral-equation based Green’s function diakoptics for time-harmonic fields, a demonstrably stable discrete space-time Green’s function diakoptics scheme has been reported to be effective for proximate regions. For distant regions it is necessary to retain a long field history. Upon considering a diakoptics toy problem involving two disjoint domains consisting of a single point each, the resulting boundary operator may be expressed in terms of two distinct discrete Green’s functions only, describing the intra- and inter-domain unitsource field responses, respectively. There are various integral representations and asymptotic expansions for the discrete Z-domain Green’s functions, and it is even possible to construct representations for the discrete space-time Green’s functions consisting of nested finite sums, which turn out to be difficult to evaluate due to severe cancellations.
|Title of host publication||Proceedings of the 2010 International Conference on Electromagnetics in Advanced Applications (ICEAA '10), September 20-24, 2010, Sydney, Australia|
|Place of Publication||Piscataway|
|Publisher||Institute of Electrical and Electronics Engineers|
|Publication status||Published - 2010|
Hon, de, B. P., & Arnold, J. M. (2010). Discrete Green's function diakoptics : a toy problem. In Proceedings of the 2010 International Conference on Electromagnetics in Advanced Applications (ICEAA '10), September 20-24, 2010, Sydney, Australia (pp. 565-568). Institute of Electrical and Electronics Engineers.